$B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 2x - 7$ and $ BC = 5x - 19$ Find $AC$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {2x - 7} = {5x - 19}$ Solve for $x$ $ -3x = -12$ $ x = 4$ Substitute $4$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 2({4}) - 7$ $ BC = 5({4}) - 19$ $ AB = 8 - 7$ $ BC = 20 - 19$ $ AB = 1$ $ BC = 1$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {1} + {1}$ $ AC = 2$